As an example of an exhaust purification device of an engine, there has been known an exhaust purification device disclosed in JP2009-197728A. Specifically, the exhaust purification device disclosed in JP2009-197728A includes: in order from an upstream of an exhaust passage, an oxidation catalyst which purifies HC or the like in an exhaust gas; a particulate filter which collects particulate matter in the exhaust gas; a urea water supply valve which injects urea water into the exhaust passage; and an SCR catalyst which purifies NOx in the exhaust gas due to a reduction action of ammonium formed from urea.
In an engine which includes the above-mentioned exhaust purification device, when deceleration fuel cut for stopping supply of fuel at the time of deceleration is performed, air of relatively low temperature which does not contain a burnt gas flows from an intake passage to an exhaust passage. As a result, a temperature of an oxidation catalyst or an SCR catalyst is gradually lowered. However, when the above-mentioned deceleration fuel cut is performed (a large amount of air passing through the oxidation catalyst or the SCR catalyst due to such deceleration fuel cut) under a condition where the temperature of the oxidation catalyst or the SCR catalyst is relatively low, as in the case of a non-warm-up period which comes immediately after starting an engine, the temperature of the oxidation catalyst or the SCR catalyst is further lowered thus giving rise to a drawback that purifying performance of each catalyst is lowered.